Rendering flipped textured backface
The Geometry node provides a Backfacing value that indicates whether the front or back face is being rendered. By using this to mix between the normal image coordinates and coordinates which have been scales by -1 in one direction we can effectively flip the image for the opposite face, "unmirroring" the image so that the same image is shown on the front and back.

This can be achieved with the following nodes :



Note the Mapping node with the Y-scale set to -1. The Mix node selects which set of input coordinates (Generated or the 'flipped' generated) are used to drive the Image Texture.



Additional...

This only works 'as-is' due to the Image Texture being set to 'Repeat'. The 'unflipped' coordinates vary in the Y coordinate from 0.0 to 1.0 and so the mapping node is translating this to 0.0 to **-**1.0 - ie, the opposite to the usual coordinates. Since the Image Texture is set to 'Repeat' this isn't a problem since the image repeats in all directions.

In order to allow this to work with 'Clipped' images you can simply use the Location settings of the Mapping node to offset Y by 1.0 (set 'Y' Location to 1.0). This will translate the 0.0 to -1.0 values to 1.0 to 0.0 (ie, reversed).